A woman who says she was threatened with being kicked off a US Delta Air Lines flight because she was not wearing a bra demanded a meeting with the company's top boss on Thursday over what she says is a discriminatory policy.

Lisa Archbold said she had on baggy jeans and a loose white t-shirt -- with no bra -- and claimed she was temporarily escorted off a flight by a female gate agent who demanded she cover up, even though her breasts were not visible.

"It felt like a scarlet letter was being attached to me," Archbold, 38, told reporters in Los Angeles about the January incident.

"I felt it was a spectacle aimed at punishing me for not being a woman in the way she thought I should be a woman as she scolded me outside of the plane."

Archbold, a DJ who was flying from Salt Lake City in conservative Utah to the famously liberal San Francisco, claims the Delta agent said her attire was "revealing" and "offensive" and that airline policy was not to allow passengers dressed that way to travel.

But, the agent said, if she put a jacket over her t-shirt, she would be allowed to continue her journey.

Attorney Gloria Allred said she had written to Delta on behalf of Archbold demanding a meeting with the company's president to discuss the discriminatory policy.

"Male passengers are not required to cover up their t-shirts with a shirt or a jacket," she said.

"They also do not have to wear a bra to board or remain on a plane and women should not have to wear one either.

"Last I checked, the Taliban are not in charge of Delta."

Allred said US federal rules allow airlines to remove passengers who present a safety or security risk to the plane or its passengers, but that was clearly not the case with Archbold.

"Neither her breasts nor any other woman's breasts have ever tried to take over a plane," she said.

"Breasts are not weapons of war, and it's not a crime for a woman or girl to have them."

Allred said there were currently no plans for a lawsuit and that all she and Archbold wanted was a meeting with Delta's president to secure assurances their policies would be updated.

In response to AFP inquiries, a spokesperson for the company said: "Earlier this year, Delta representatives contacted this customer with an apology."